387 research outputs found
Machine learning and privacy preserving algorithms for spatial and temporal sensing
Sensing physical and social environments are ubiquitous in modern mobile phones,
IoT devices, and infrastructure-based settings. Information engraved in such
data, especially the time and location attributes have unprecedented potential
to characterize individual and crowd behaviour, natural and technological processes.
However, it is challenging to extract abstract knowledge from the data
due to its massive size, sequential structure, asynchronous operation, noisy characteristics,
privacy concerns, and real time analysis requirements. Therefore, the
primary goal of this thesis is to propose theoretically grounded and practically
useful algorithms to learn from location and time stamps in sensor data. The
proposed methods are inspired by tools from geometry, topology, and statistics.
They leverage structures in the temporal and spatial data by probabilistically
modeling noise, exploring topological structures embedded, and utilizing statistical
structure to protect personal information and simultaneously learn aggregate
information. Proposed algorithms are geared towards streaming and distributed
operation for efficiency. The usefulness of the methods is argued using mathematical
analysis and empirical experiments on real and artificial datasets
Constraints on quasi-normal-mode frequencies with LIGO-Virgo binary-black-hole observations
The no-hair conjecture in General Relativity (GR) states that a Kerr black
hole (BH) is completely described by its mass and spin. As a consequence, the
complex quasi-normal-mode (QNM) frequencies of a binary-black-hole (BBH)
ringdown can be uniquely determined by the mass and spin of the remnant object.
Conversely, measurement of the QNM frequencies could be an independent test of
the no-hair conjecture. This paper extends to spinning BHs earlier work that
proposed to test the no-hair conjecture by measuring the complex QNM
frequencies of a BBH ringdown using parameterized inspiral-merger-ringdown
waveforms in the effective-one-body formalism, thereby taking full advantage of
the entire signal power and removing dependency on the predicted or estimated
start time of the ringdown. Our method was used to analyze the properties of
the merger remnants for BBHs observed by LIGO-Virgo in the first half of their
third observing (O3a) run. After testing our method with GR and non-GR
synthetic-signal injections in Gaussian noise, we analyze, for the first time,
two BBHs from the first (O1) and second (O2) LIGO-Virgo observing runs, and two
additional BBHs from the O3a run. We then provide joint constraints with
published results from the O3a run. In the most agnostic and conservative
scenario where we combine the information from different events using a
hierarchical approach, we obtain, at credibility, that the fractional
deviations in the frequency (damping time) of the dominant QNM are (),
respectively, an improvement of a factor of () over the
results obtained with our model in the LIGO-Virgo publication. The single-event
most-stringent constraint to date continues to be GW150914 for which we obtain
and .Comment: 15 pages, 8 figure
Constraining extra dimensions using observations of black hole quasi-normal modes
The presence of extra dimensions generically modify the spacetime geometry of
a rotating black hole, by adding an additional hair, besides the mass and
the angular momentum , known as the `tidal charge' parameter, . In a
braneworld scenario with one extra spatial dimension, the extra dimension is
expected to manifest itself through -- (a) negative values of , and (b)
modified gravitational perturbations. This in turn would affect the
quasi-normal modes of rotating black holes. We numerically solve the perturbed
gravitational field equations using the continued fractions method and
determine the quasi-normal mode spectra for the braneworld black hole. We find
that increasingly negative values of correspond to a diminishing
imaginary part of the quasi-normal mode, or equivalently, an increasing damping
time. Using the publicly available data of the properties of the remnant black
hole in the gravitational wave signal GW150914, we check for consistency
between the predicted values (for a given ) of the frequency and damping
time of the least-damped quasi-normal mode and measurements of
these quantities using other independent techniques. We find that it is highly
unlikely for the tidal charge, , providing a conservative
limit on the tidal charge parameter. Implications and future directions are
discussed.Comment: 11 pages, 2 figures, 1 table, Revised version accepted in EPJ
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